derivative f(x)=6\sqrt[3]{x}

Lösung

ableitung von

f (x) = 6 3 x

\frac{2}{x ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (6 3 x)

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (3 x)

Wende Radikal Regel an:

n a = a^{\frac{1}{n}}

= 6 \frac{d}{d x} (x^{\frac{1}{3}})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 6 \cdot \frac{1}{3} x^{\frac{1}{3} - 1}

Vereinfache

6 \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{2}{x ^{\frac{2}{3}}}

= \frac{2}{x ^{\frac{2}{3}}}

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